The International Organisation for Migration said it was the biggest single loss of life in the Channel since it began collecting data in 2014.
Prime Minister Boris Johnson said he was "appalled" by what happened, adding the UK would leave "no stone unturned" to stop human trafficking gangs.
He will chair an emergency Cobra meeting this evening on the issue.
LIVE UPDATES: Rescue operation in Channel as migrants drown
What happens to migrants who reach the UK?
A fishing boat sounded the alarm on Wednesday afternoon after spotting several people at sea off the coast of France.
French and British authorities are conducting a rescue operation by air and sea to see if they can find anyone.
Mr Johnson said the deaths were a "disaster", adding that it was vital to "break" the people trafficking gangs which, he said, were "literally getting away with murder".
He said more needed to be done to stop criminals organising crossings.
The PM said: "It also shows how vital it is that we now step up our efforts to break the business model of the gangsters who are sending people to sea in this way."
French prime minister Jean Castex said the shipwreck was a "tragedy" and those who died were victims of "criminal smugglers".
"My thoughts are with the many missing and injured, victims of criminal smugglers who exploit their distress and injury," he said.
Conservative MP for Dover and Deal, Natalie Elphicke, said the incident was an "absolute tragedy" that underlined why boats needed to be stopped from entering the water.
"As winter is approaching the seas will get rougher, the water colder, the risk of even more lives tragically being lost greater," she said. "That's why stopping these dangerous crossings is the humanitarian and right thing to do."
A number of people are believed to have reached the UK in small boats on Wednesday, with people seen being brought ashore in Dover by immigration officials.
BBC Newsnight's policy editor, Lewis Goodall, said he understood about 25 boats had attempted the crossing so far during the day.
He added that an aid agency warned there was a risk the Channel could become a "graveyard".
Chart showing numbers of migrants crossing the Channel in small boats to 2021
It comes amid record numbers of migrants making the crossing from France to the UK. More than 25,700 people have made the dangerous journey to the UK in small boats this year - more than three times the 2020 total.
The Dover Strait is the busiest shipping lane in the world and has claimed many lives of people trying to cross to Britain in inflatable dinghies.
It is thought at least 10 other people had died in the past few weeks while attempting to make the crossing.
The International Organisation for Migration said it was the biggest single loss of life in the Channel since it began collecting data in 2014.
Prime Minister Boris Johnson said he was "appalled" by what happened, adding the UK would leave "no stone unturned" to stop human trafficking gangs.
He will chair an emergency Cobra meeting this evening on the issue.
LIVE UPDATES: Rescue operation in Channel as migrants drown
What happens to migrants who reach the UK?
A fishing boat sounded the alarm on Wednesday afternoon after spotting several people at sea off the coast of France.
French and British authorities are conducting a rescue operation by air and sea to see if they can find anyone.
Mr Johnson said the deaths were a "disaster", adding that it was vital to "break" the people trafficking gangs which, he said, were "literally getting away with murder".
He said more needed to be done to stop criminals organising crossings.
The PM said: "It also shows how vital it is that we now step up our efforts to break the business model of the gangsters who are sending people to sea in this way."
French prime minister Jean Castex said the shipwreck was a "tragedy" and those who died were victims of "criminal smugglers".
"My thoughts are with the many missing and injured, victims of criminal smugglers who exploit their distress and injury," he said.
Conservative MP for Dover and Deal, Natalie Elphicke, said the incident was an "absolute tragedy" that underlined why boats needed to be stopped from entering the water.
"As winter is approaching the seas will get rougher, the water colder, the risk of even more lives tragically being lost greater," she said. "That's why stopping these dangerous crossings is the humanitarian and right thing to do."
A number of people are believed to have reached the UK in small boats on Wednesday, with people seen being brought ashore in Dover by immigration officials.
BBC Newsnight's policy editor, Lewis Goodall, said he understood about 25 boats had attempted the crossing so far during the day.
He added that an aid agency warned there was a risk the Channel could become a "graveyard".
Chart showing numbers of migrants crossing the Channel in small boats to 2021
It comes amid record numbers of migrants making the crossing from France to the UK. More than 25,700 people have made the dangerous journey to the UK in small boats this year - more than three times the 2020 total.
The Dover Strait is the busiest shipping lane in the world and has claimed many lives of people trying to cross to Britain in inflatable dinghies.
It is thought at least 10 other people had died in the past few weeks while attempting to make the crossing.
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